airGR (version 1.7.6)

ErrorCrit_KGE2: Error criterion based on the KGE' formula

Description

Function which computes an error criterion based on the KGE' formula proposed by Kling et al. (2012).

Usage

ErrorCrit_KGE2(InputsCrit, OutputsModel, warnings = TRUE, verbose = TRUE)

Value

[list] list containing the function outputs organised as follows:

$CritValue	[numeric] value of the criterion
$CritName	[character] name of the criterion
$SubCritValues	[numeric] values of the sub-criteria
$SubCritNames	[character] names of the components of the criterion
$CritBestValue	[numeric] theoretical best criterion value
$Multiplier	[numeric] integer indicating whether the criterion is indeed an error (+1) or an efficiency (-1)
$Ind_notcomputed	[numeric] indices of the time steps where InputsCrit$BoolCrit = FALSE or no data is available

Arguments

InputsCrit

[object of class InputsCrit] see CreateInputsCrit for details

OutputsModel

[object of class OutputsModel] see RunModel_GR4J or RunModel_CemaNeigeGR4J for details

warnings

(optional) [boolean] boolean indicating if the warning messages are shown, default = TRUE

verbose

(optional) [boolean] boolean indicating if the function is run in verbose mode or not, default = TRUE

Author

Laurent Coron, Olivier Delaigue

Details

In addition to the criterion value, the function outputs include a multiplier (-1 or +1) which allows the use of the function for model calibration: the product \(CritValue \times Multiplier\) is the criterion to be minimised (Multiplier = -1 for KGE2).

The KGE' formula is $$KGE' = 1 - \sqrt{(r - 1)^2 + (\gamma - 1)^2 + (\beta - 1)^2}$$ with the following sub-criteria: $$r = \mathrm{the\: linear\ correlation\: coefficient\: between\:} sim\: \mathrm{and\:} obs$$ $$\gamma = \frac{CV_{sim}}{CV_{obs}}$$ $$\beta = \frac{\mu_{sim}}{\mu_{obs}}$$

References

Gupta, H. V., Kling, H., Yilmaz, K. K. and Martinez, G. F. (2009). Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of Hydrology, 377(1-2), 80-91, tools:::Rd_expr_doi("10.1016/j.jhydrol.2009.08.003").

Kling, H., Fuchs, M. and Paulin, M. (2012). Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. Journal of Hydrology, 424-425, 264-277, tools:::Rd_expr_doi("10.1016/j.jhydrol.2012.01.011").

See Also

ErrorCrit, ErrorCrit_RMSE, ErrorCrit_NSE, ErrorCrit_KGE

Examples

library(airGR)

## loading catchment data
data(L0123001)

## preparation of the InputsModel object
InputsModel <- CreateInputsModel(FUN_MOD = RunModel_GR4J, DatesR = BasinObs$DatesR,
                                 Precip = BasinObs$P, PotEvap = BasinObs$E)

## run period selection
Ind_Run <- seq(which(format(BasinObs$DatesR, format = "%Y-%m-%d")=="1990-01-01"),
               which(format(BasinObs$DatesR, format = "%Y-%m-%d")=="1999-12-31"))

## preparation of the RunOptions object
RunOptions <- CreateRunOptions(FUN_MOD = RunModel_GR4J,
                               InputsModel = InputsModel, IndPeriod_Run = Ind_Run)

## simulation
Param <- c(X1 = 734.568, X2 = -0.840, X3 = 109.809, X4 = 1.971)
OutputsModel <- RunModel(InputsModel = InputsModel, RunOptions = RunOptions,
                         Param = Param, FUN = RunModel_GR4J)

## efficiency criterion: Kling-Gupta Efficiency
InputsCrit <- CreateInputsCrit(FUN_CRIT = ErrorCrit_KGE2, InputsModel = InputsModel,
                               RunOptions = RunOptions, Obs = BasinObs$Qmm[Ind_Run])
OutputsCrit <- ErrorCrit_KGE2(InputsCrit = InputsCrit, OutputsModel = OutputsModel)

## efficiency criterion: Kling-Gupta Efficiency on square-root-transformed flows
transfo <- "sqrt"
InputsCrit <- CreateInputsCrit(FUN_CRIT = ErrorCrit_KGE2, InputsModel = InputsModel,
                               RunOptions = RunOptions, Obs = BasinObs$Qmm[Ind_Run],
                               transfo = transfo)
OutputsCrit <- ErrorCrit_KGE2(InputsCrit = InputsCrit, OutputsModel = OutputsModel)

## efficiency criterion: Kling-Gupta Efficiency above a threshold (quant. 75 %)
BoolCrit <- BasinObs$Qmm[Ind_Run] >= quantile(BasinObs$Qmm[Ind_Run], 0.75, na.rm = TRUE)
InputsCrit <- CreateInputsCrit(FUN_CRIT = ErrorCrit_KGE2, InputsModel = InputsModel,
                               RunOptions = RunOptions, Obs = BasinObs$Qmm[Ind_Run],
                               BoolCrit = BoolCrit)
OutputsCrit <- ErrorCrit_KGE2(InputsCrit = InputsCrit, OutputsModel = OutputsModel)